%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP403-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:28:47 AM UTC 2026
% Result : Unsatisfiable 0.21s 5.95s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 23 ( 23 unt; 0 def)
% Number of atoms : 23 ( 22 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 10 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,inverse(multiply(inverse(multiply(inverse(multiply(VAR_0,VAR_1)),VAR_2)),inverse(multiply(VAR_1,multiply(inverse(VAR_1),VAR_1)))))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),inverse(multiply(B,multiply(inverse(B),B)))))) = C,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(prove_these_axioms_1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('theBenchmark.p',prove_these_axioms_1) ).
cnf(c_2,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(clausify,[status(thm)],[prove_these_axioms_1]) ).
cnf(c_3,plain,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
inference(copy,[status(thm)],[c_2]) ).
cnf(c_82,plain,
multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,multiply(inverse(C),C)))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,C)),D)),B)),inverse(multiply(D,multiply(inverse(D),D))))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_4,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),D)),inverse(multiply(C,multiply(inverse(C),C))))) = multiply(A,inverse(multiply(inverse(D),inverse(multiply(B,multiply(inverse(B),B)))))),
inference(copy,[status(thm)],[c_82]) ).
cnf(c_5,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(C),inverse(multiply(B,multiply(inverse(B),B))))))) = C,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_83,plain,
multiply(inverse(multiply(A,B)),multiply(A,multiply(C,inverse(multiply(inverse(D),inverse(multiply(E,multiply(inverse(E),E)))))))) = multiply(inverse(multiply(inverse(multiply(C,E)),B)),D),
inference(paramod,[status(thm)],[c_4,c_5]) ).
cnf(c_6,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),C)),D) = multiply(inverse(multiply(E,C)),multiply(E,multiply(A,inverse(multiply(inverse(D),inverse(multiply(B,multiply(inverse(B),B)))))))),
inference(copy,[status(thm)],[c_83]) ).
cnf(c_7,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(A,B)),D)) = multiply(inverse(multiply(E,C)),multiply(E,D)),
inference(paramod,[status(thm)],[c_1,c_6]) ).
cnf(c_84,plain,
inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(B,multiply(inverse(B),B))))) = multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(D,E)),C)),inverse(multiply(E,multiply(inverse(E),E)))))),
inference(paramod,[status(thm)],[c_7,c_4]) ).
cnf(c_11,plain,
inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(B,multiply(inverse(B),B))))) = C,
inference(paramod,[status(thm)],[c_1,c_84]) ).
cnf(c_85,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,multiply(E,inverse(multiply(inverse(multiply(inverse(multiply(E,F)),C)),inverse(multiply(F,multiply(inverse(F),F)))))))),
inference(paramod,[status(thm)],[c_7,c_6]) ).
cnf(c_12,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(paramod,[status(thm)],[c_1,c_85]) ).
cnf(c_86,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(C,inverse(multiply(B,multiply(inverse(B),B))))))) = multiply(inverse(multiply(inverse(multiply(D,E)),multiply(D,C))),inverse(multiply(E,multiply(inverse(E),E)))),
inference(paramod,[status(thm)],[c_11,c_5]) ).
cnf(c_25,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(B,multiply(inverse(B),B)))) = multiply(inverse(multiply(D,E)),multiply(D,inverse(multiply(C,inverse(multiply(E,multiply(inverse(E),E))))))),
inference(copy,[status(thm)],[c_86]) ).
cnf(c_87,plain,
multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,A))),D)) = multiply(inverse(multiply(E,inverse(multiply(C,multiply(inverse(C),C))))),multiply(E,D)),
inference(paramod,[status(thm)],[c_11,c_12]) ).
cnf(c_26,plain,
multiply(inverse(multiply(A,inverse(multiply(B,multiply(inverse(B),B))))),multiply(A,C)) = multiply(D,multiply(inverse(multiply(inverse(multiply(E,B)),multiply(E,D))),C)),
inference(copy,[status(thm)],[c_87]) ).
cnf(c_47,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),inverse(multiply(B,multiply(inverse(B),B)))) = C,
inference(paramod,[status(thm)],[c_25,c_5]) ).
cnf(c_56,plain,
multiply(inverse(multiply(A,inverse(multiply(B,multiply(inverse(B),B))))),multiply(A,inverse(multiply(B,multiply(inverse(B),B))))) = multiply(inverse(C),C),
inference(paramod,[status(thm)],[c_47,c_26]) ).
cnf(c_80,plain,
multiply(inverse(multiply(A,inverse(multiply(B,multiply(inverse(B),B))))),multiply(A,inverse(multiply(B,multiply(inverse(B),B))))) != multiply(inverse(a1),a1),
inference(paramod,[status(thm)],[c_56,c_3]) ).
cnf(c_81,plain,
$false,
inference(resolve,[status(thm)],[c_80,c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP403-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/5.42 % Computer : n011.cluster.edu
% 0.15/5.42 % Model : x86_64 x86_64
% 0.15/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.42 % Memory : 8046.5625MB
% 0.15/5.42 % OS : Linux 6.8.0-71-generic
% 0.15/5.42 % CPULimit : 300
% 0.15/5.42 % WCLimit : 300
% 0.15/5.42 % DateTime : Fri Sep 25 14:52:20 UTC 2026
% 0.15/5.42 % CPUTime :
% 0.15/5.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/5.43 % Process 2284322 was started by sandbox2 on n011,
% 0.15/5.43 % Fri Sep 25 14:52:20 2026
% 0.15/5.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/5.43
% 0.15/5.43 % From the command line: assign(max_seconds, 300).
% 0.21/5.95
% 0.21/5.95 % SZS status Unsatisfiable for theBenchmark
% 0.21/5.95
% 0.21/5.95 % Proof 1 at 0.40 (+ 0.11) seconds.
% 0.21/5.95 % Length of proof is 15.
% 0.21/5.95 % Level of proof is 10.
% 0.21/5.95 % Maximum clause weight is 100.000.
% 0.21/5.95 % Given clauses 33.
% 0.21/5.95
% 0.21/5.95 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------